Wilkinson, who kicked the drop goal that gave England victory in last November's World Cup final against Australia, had the operation in February.
"I didn't realise how close I was to not playing again," Wilkinson told the Times on Tuesday.
Wilkinson last played in December but the Falcons website said that the 25-year-old had been training for some time and had been given the all clear to take a full part in their pre-season.
The Times said that Wilkinson hoped to make his comeback on August 17 when Newcastle start their pre-season tour of Ireland with a match against Connacht.
"I'll begin contact work next week," Wilkinson said.
"If there was a game next week then I would have done my collision contact work already and I'd be able to take some hits."
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"I know I haven't got a bad neck any more and that's the first time I've been able to say that since I was 14."
England have lost five of their eight matches since Wilkinson was injured, including all three on their recent tour of Australia and New Zealand.